This project work focuses on the possibility of coexistence of superconductivity and magnetism in Samarium arsenide oxide superconductor (SmO1-xFxFeAs). Using the model Hamiltonian and retarded double time temperature dependent Green's function formalism, we derived the mathematical expressions for the superconducting critical temperature ( ), superconducting order parameter ( ), the magnetic order parameter (η) and magnetic ordering temperature ( ). Using the equations derived, we plotted the phase diagrams and by merging the phase diagram of the superconducting critical temperature ( ) versus the magnetic order parameter (η) and the phase diagram of magnetic ordering temperature ( ) versus the magnetic order parameter (η), we showed the region where both superconductivity and antiferromagnetism coexist. The results obtained are in broad agreement with the experimental findings. Key words: Critical temperature: The temperature below which the electrical resistance of materials goes to zero. Superconductivity: The phenomenon of exactly zero electrical resistance and expulsion of magnetic field occurring in a certain materials when cooled below a critical temperature